To prepare 500 mL of a solution with a specific concentration from a stock solution with a higher concentration, we use the principles of dilution.
1. Determine the desired concentration: Suppose we want to prepare a 1.0 M solution of [tex]\( H_3O_3 \)[/tex]. This is a standard assumption to demonstrate how to prepare a solution of a desired concentration.
2. Volume of desired solution: We are aiming to make 500 mL (0.500 L) of this solution.
3. Stock solution concentration: The stock solution has a concentration of 17.4 M.
Using the dilution formula:
[tex]\[ M_1 \times V_1 = M_2 \times V_2 \][/tex]
Where [tex]\( M_1 \)[/tex] is the molarity of the stock solution, [tex]\( V_1 \)[/tex] is the volume of the stock solution needed, [tex]\( M_2 \)[/tex] is the molarity of the desired solution, and [tex]\( V_2 \)[/tex] is the volume of the desired solution.
Rearrange this formula to solve for [tex]\( V_1 \)[/tex]:
[tex]\[ V_1 = \frac{M_2 \times V_2}{M_1} \][/tex]
4. Substitute the known values:
[tex]\[ V_1 = \frac{1.0 \times 500}{17.4} \][/tex]
[tex]\[ V_1 \approx 28.73563218390805 \, \text{mL} \][/tex]
Thus, to prepare 500 mL of 1.0 M solution, you need approximately 28.74 mL of the 17.4 M stock solution.
5. Calculate the volume of water needed to dilute the stock solution:
Subtract the volume of the stock solution from the total desired volume:
[tex]\[ \text{Volume of water} = 500 \, \text{mL} - 28.74 \, \text{mL} \][/tex]
[tex]\[ \text{Volume of water} \approx 471.264367816092 \, \text{mL} \][/tex]
So, to prepare the 500 mL of the desired 1.0 M [tex]\( H_3O_3 \)[/tex] solution, you should:
- Measure 28.74 mL of the 17.4 M stock solution.
- Add this stock solution to a volumetric flask.
- Add water until the total volume in the flask reaches 500 mL.
This will yield 500 mL of a 1.0 M [tex]\( H_3O_3 \)[/tex] solution.
